Twenty-Seventh Symposium (International) on Combustion/The Combustion Institute, 1998/pp. 2351–2357
THERMAL DECOMPOSITION OF GASEOUS AMMONIUM DINITRAMIDE AT
LOW PRESSURE: KINETIC MODELING OF PRODUCT FORMATION WITH
ab initio MO/cVRRKM CALCULATIONS
J. PARK, D. CHAKRABORTY and M. C. LIN
Department of Chemistry
Emory University
Atlanta, GA 30322, USA
The thermal decomposition of ammonium dinitramide, NH4N(NO2)2 (ADN), in the gas phase has been
studied at 373–920 K by pyrolysis/mass spectrometry under low-pressure conditions using a Saalfeld reactor. The reaction of the sublimed mixture of NH3 and HN(NO2)2 (dinitraminic acid, DN) was found to
be initiated by the unimolecular decomposition of DN, HN(NO2)2 → HNNO2 ` NO2, followed by the
rapid decomposition reaction, HNNO2 ` M → N2O ` OH ` M. The measured absolute yields of NH3,
H2O, N2, and N2O, calibrated with standard mixtures, could be satisfactorily modeled at 10 Torr He carrier
gas pressure by employing the theoretically computed values of k2 4 6.79 2 1048 T111.0 exp(121780/T)
s11 and k3 4 7.53 2 1024 T12.9 exp(112958/T) cm3/(mol s) by high-level ab initio molecular orbital and
canonical variational Rice-Ramsperger-Kassel-Marcus (MO/cVRRKM) calculations. The key reactions with
recommended rate constants are presented.
Introduction
There has been an avalanche of research activity
on the kinetics and mechanism of the ammonium
dinitramide (ADN) decomposition reaction [1–9]
since the earlier studies of Brill, Rossi, and coworkers [1,2]. The majority of these studies focuses on
product detection, typically at temperatures above
its melting point, 365 5 1 K, under pressurized conditions where both gaseous and condensed-phase
species are involved in the overall decomposition
process. The results of these studies, including the
latest papers by Oxley [7], Wight [8,9] and their collaborators, reported the observation of rapid production of varying quantities of nitrogen oxides (NO,
NO2, and N2O) with the apparent activation energy
for the overall disappearance of ADN to be in the
range of 40–48 kcal/mol.
By T-jump Fourier transform infrared (FTIR)
spectroscopy, Brill and coworkers [1] detected the
fast appearance of NH3, N2O, NO2, H2O, and
HNO3 under 1 atm Ar. They proposed the following
two branches of global decomposition reactions:
ADN(s) → NH3 ` HN(NO2)2
(1a)
→ NH3 ` N2O ` HNO3
(1b)
The decomposition of dinitraminic acid (DN) and
reactions of its fragments may qualitatively yield
from branch (1a) the global product stoichiometry:
9ADN → 6 NH3 ` 7N2O ` 10NO2 ` 9H2O `
3N2 [1].
In a similar qualitative study by Rossi et al. [2],
carried out under high-vacuum (1017 Torr) conditions by FTIR spectroscopy for the detection of frozen products on a cold KCl window and by mass
spectrometry for the analysis of residual gases, the
decomposition of ADN in a Pyrex capillary tube
heated to 443 K was found to produce predominantly NH3, N2O, NO, H2O, and a comparable
amount of DN.
To elucidate the mechanism of the ADN decomposition reaction, we had earlier investigated the
thermochemistry of the system by high-level ab initio molecular orbital (MO) calculations [10]. The
results of this study led us to the conclusion, similar
to that reached by Politzer and coworkers [11,12],
that ADN is unstable in ionic form, NH`
4
N(NO2)1
2 , and its sublimation leads to the formation
of two molecular complexes, H3N • HN(NO2)2 and
H3N • HON(O)NNO2, which are more stable than
the dissociated states, NH3 ` HN(NO2)2 and NH3
` HON(O)NNO2, by 12.4 and 14.1 kcal/mol, respectively. The former DN isomer was calculated at
the Gaussian-1 (G1) level of theory to have 38.4 kcal/
mol dissociation energy producing NO2 ` HNNO2,
whereas the latter DN8 isomer has a dissociation energy of 40.1 kcal/mol yielding NO2 ` HON(O)N.
The overall energy difference for the formation of
DN and DN8 from ADN(s) was predicted to be 4.2
kcal/mol, which gives an DN/DN8 isomeric ratio of
3 2 1013 at the sublimation temperature T 4 362
K, about 38 below its melting point. Because the
DN8 isomer can undergo the isomerization/decomposition reaction producing HNO3 ` N2O via a
2351
2352
PROPELLANTS
four-centered transition state [10], the apparent enrichment of ADN(s) with AN(s, ammonium nitrate)
by the sublimation/decomposition process can be
readily understood.
In this study, we focus our kinetic measurements
under low-pressure conditions and in the early
stages of sample sublimation by pyrolysis/mass spectrometry so as to elucidate the overall gas-phase reaction mechanism:
ADN(s) → NH3 ` HN(NO2)2 → products
The rates of formation of the products that can be
unambiguously measured and quantitatively calibrated (N2, N2O, H2O, and NH3) are kinetically
modeled. The results of this study, aided by our new
high-level ab initio MO/statistical-theory calculations for the unimolecular decomposition of DN and
HNNO2, are reported here.
Experimental Procedure
The study of the thermal decomposition reaction
of sublimed ADN was carried out by using a pyrolysis/mass spectrometric technique in the temperature range 373–920 K. The schematic diagram for
the experiment is shown in Fig. 1. The description
of the supersonic mass-spectrometric sampling technique, first used by Saalfeld and coworkers [13], has
been given elsewhere [14,15]. Only a brief description of the sublimation process will be given here.
The sublimation of ADN took place in a thermostatted sample holder. To achieve homogeneous heating of the sample, we used continuously circulated
hot ethylene glycol–water solution using a NESLAB
RTC-110 temperature controller that has an accuracy and reproducibility of 0.3 K. The pyrolysis of
the sublimed ADN sample entrained with 10 Torr
He carrier gas was performed under slow-flow conditions in a Saalfeld-type quartz tubular reactor tube
[13], which has an inner diameter of 10 mm and a
length of 150 mm with a conical sampling hole at
the center. The reactor was mounted perpendicularly to the detection axis of a quadrupole mass spectrometer (QMS, Extrel Model C50), and the reaction tube was wrapped with a 15-mm-thick,
15-mm-wide Nichrome ribbon and insulated with
ceramic wool. The reactor temperature could be varied from 300 to 1000 K by adjusting the current
through the heater. To minimize heterogeneous surface effects, the inner wall of the reactor was pretreated with boric acid, followed by an extensive
bake-out at 1000 K under high vacuum.
The detection chamber housing the mass spectrometer was separated from the supersonic expansion chamber by a metal plate with a 1.0-mm orifice
skimmer (Beam Dynamics Model 1) mounted at the
center of the plate. The supersonically expanded
molecular beam was introduced through the skimmer into the ionization region of the spectrometer.
During the experiment, the pressures in the reaction
and detection chambers were maintained at (5–10)
2 1015 and (5–10) 2 1016 Torr, respectively.
ADN samples were obtained from the Naval Surface Warfare Center with a purity of 97% to 99%
ADN and 3% to 1 % AN (ammonium nitrate); they
were used without further purification. NH3, H2O
(deionized water), and N2O were purified by standard trap-to-trap distillation. He and N2 (99.9995%,
UHP, Specialty Gases) were used without further
purification. After an ADN sample was introduced
into the reaction system, it was typically evacuated
under high vacuum for several days to minimize water contamination.
The absolute concentrations of NH3, N2, N2O,
and H2O were calibrated with carefully prepared
standard mixtures. The initial concentrations of DN,
generated by the sublimation of ADN at 362 K, were
assumed to be the same as that of NH3 measured
with the reactor temperature set at 373 K, at which
no reaction was found to occur.
Results and Discussion
Ab Initio MO/cVRRKM Calculations
Geometries of NO2, HNNO2, and DN have been
optimized at the hybrid density functional B3LYP/6311G(d,p) level of theory, based on the Becke threegrid integration and exchange functional [16–18]
with the correlation functional by Lee et al. [19].
Vibrational frequencies employed to characterize
stationary points, zero-point energies (ZPE), and
rate constant calculations have also been calculated
at this level of theory. To obtain a more accurate
description of the reaction path, we used the
G2M(RCC,MP2) method of Mebel et al. [20], which
approaches high-level results using a series of singlepoint calculations for basis set size, correlation energy, and systematic error corrections. All calculations were carried out with the Gaussian 94 program
[21].
Because the reaction path for the decomposition
of DN does not have a well-defined transition state
(TS) because of the absence of a reaction barrier, we
applied here the canonical variational method based
on the evaluation of the maximum free energy of
activation (DG#) at each temperature along the reaction path [22–25]. We scanned the potential energy surface for the dissociation of DN to HNNO2
and NO2 at the B3LYP level. The dissociating N–N
bond distance of DN was varied from 1.8 A. to 3.0
A. with an interval of 0.1 A. ; other geometric parameters were optimized for each value of the N–N separation. For each structure, we calculated the 3N-7
vibrational frequencies projected out of the gradient
direction. This B3LYP calculated energy at each
point along the reaction path was used to evaluate
DECOMPOSITION OF AMMONIUM DINITRAMIDE: MODELING
2353
Fig. 1. Schematic diagram of the
experimental apparatus.
to search for the maximum Gibbs free energy
change (DG#) at various temperatures in the range
of 300 to 1000 K. The accurate position of the maximum for each temperature was calculated on the
basis of the parabolic fit to the three largest DG values. All the molecular parameters corresponding to
the structure with a DG# for each temperature were
then used for the RRKM calculation. As the DG#
maxima along the reaction path are located between
the calculated structures, the corresponding moments of inertia and vibrational frequencies were obtained by interpolation [23,24]. The high-pressure
rate constant for the decomposition of DN is related
to DG# by the well-known equation:
k`2 4 (kBT/h) exp(1DG#/RT)
Fig. 2. Arrhenius plots for the DN decomposition (a)
and its reverse association (b) reactions.
k`2 4 1.92 2 1017 exp(118300/T) s11
the Morse potential energy function and then scaled
by using the scale factor obtained by comparing N–
N dissociation energies at G2M and B3LYP levels.
The Morse potential energy was given by the following formula:
E(r) 4 De [1 1 e
1b(R1Re)
]2
(I)
with De 4 37.9 kcal/mol, Re 4 1.463 Å, and b 4
2.42 A. 11. The dissociation energy obtained by the
G2M method, 37.9 kcal/mol, agrees very well with
the G1 calculated value of Mebel et al., 38.4 kcal/
mol [10]. The computed moments of inertia, the vibrational frequencies, and the dissociation energy
given in the preceding as a function of R were used
(II)
where kB is the Boltzmann constant and h the Planck
constant [26].
Vibrational modes with frequencies below 50
cm11 were treated as free internal rotations for both
DN and the transition state. The calculated decomposition and reverse association rate constants for
DN are shown in Fig. 2. Least-squares analysis of
rate constants for the decomposition process at the
high-pressure limit, 200 atm, 1 atm, and 1.32 2
1012 atm (10 Torr) for He or Ar as diluent can be
represented by the following expressions:
(III)
k2 (200 atm) 4 6.88 2 1016
2 exp(118330/T) s11
k2 (1 atm) 4 1.90 2
1041
T
2 exp(121500/T) s11
k2 (10 torr) 4 6.79 2
(IV)
18.1
(V)
1048T111.0
2 exp(121780/T) s11
(VI)
for the temperature range 300–1000 K. Equation VI
was used in our kinetic modeling of the experimental
data.
2354
PROPELLANTS
Fig. 3. Mass spectra of the ADN decomposition products at different reaction temperatures as indicated.
kinetic modeling of higher temperature results. Because the DN8 isomer concentration was estimated
to be about 0.3% that of DN, its contribution to the
formation of various species measured was neglected.
The residence (or reaction) time was calculated
with the measured flow rate (F in units of standard
cubic centimeter per minute, sccm) based on the
ideal gas law, t(s) 4 (273 2 60/760) (PV/FT), where
V is the volume of the reactor in cm3, P is the total
reaction pressure (typically 10 Torr), and T is the
reactor temperature.
As indicated, our kinetic modeling was performed
with the assumption that [NH3]0 4 [DN]0 and the
reaction were initiated by the unimolecular decomposition of DN followed by the rapid isomerization/
dissociation of HNNO2, the nitro-amino radical:
HN(NO2)2 → HNNO2 ` NO2
(2)
Kinetic Modeling of the ADN Decomposition
Reaction
HNNO2 ` M → N2O ` OH ` M
(3)
Thermal decomposition of ADN, sublimed at the
constant temperature of 362 K and carried into a
preheated Saalfeld reactor with 10 Torr He carrier
gas, was studied in the temperature range 373–920
K. The mass spectra covering m/z 4 10–50 obtained
at 373, 720, and 920 K reactor temperatures are presented in Fig. 3. No noticeable peaks beyond m/z 4
50 were observed within our detectivity. As the reaction does not take place below 450 K in our timescale (t # 40 ms), the concentration of NH3 (assumed
to be equal to that of DN) and the small concentration of N2O (Fig. 4, vide infra) were used as the
initial concentrations of the reactants present for the
HNNO2 ` M → NH ` NO2 ` M
(4)
with k3 k k4, according to the result of our ab initio
MO/cVRRKM calculations [27]. For kinetic modeling, we employed 152 reactions that have been
utilized in our previous studies of the NHx ` NOy
(x 4 2,3; y 4 1,2) reactions [14,15,28,29] except
those involving DN and HNNO2. The key reactions
used in the modeling are presented in Table 1.
The results of the modeling, accomplished by using the rate of the initiation reaction 2 computed for
the 10 Torr pressure given by equation VI, are presented in Fig. 4 by the solid curves. The agreement
TABLE 1
The key reactions and rate constantsa for the kinetic modeling of the sublimed ADN system
Reaction
1a. NH4N(NO2)2 4 NH3 ` HN(NO2)2
1b. NH4N(NO2)2 4 NH3 ` N2O ` HNO3
2. HN(NO2)2 4 HNNO2 ` NO2
3. HNNO2 ` M 4 N2O ` OH ` M
4. HNNO2 ` M 4 NH ` NO2 ` M
5. OH ` NH3 4 H2O ` NH2
6. OH ` OH 4 H2O ` O
7. HNNO2 ` NO2 4 HNO ` NO ` NO2
8. HNNO2 ` OH 4 H2O ` 2NO
9. HNNO2 ` OH 4 HNO ` HONO
10. NH2 ` NO2 4 H2NO ` NO
11. NH2 ` NO2 4 N2O ` H2O
A
6.79E ` 48
7.53E ` 24
6.35E ` 18
2.00E ` 06
4.30E ` 03
3.00E ` 12
5.00E ` 12
5.00E ` 12
6.56E ` 16
1.54E ` 16
n
sublimation
sublimation
111.0
12.9
11.1
2.1
2.7
0
0
0
11.5
11.5
Ea
43277b
25750c
39397c
566
12486
0
0
0
268
268
constants, defined by k 4 ATn exp(1Ea/RT), are given in units of cm3, mole, and s; Ea is in units of cal/mol.
rate coefficient for 10 Torr He.
cRef. [24].
aRate
bFirst-order
DECOMPOSITION OF AMMONIUM DINITRAMIDE: MODELING
2355
N2 and NH3 in our modeling, and only a small decrease (,10%) in N2O and H2O yields, resulting primarily from the decrease in the rate of reactions (3).
The results of this test are given by dashed curves in
Fig. 4. It should be mentioned that the total replacement of DN by HNO3 resulted in the absence of
chemical reaction under the conditions employed.
Key Elementary Reactions
The following elementary reactions play a key role
in the decomposition of ADN under low-pressure
conditions.
Chain initiation reactions:
Fig. 4. Comparison of experimental data and kinetic
modeling results for the sublimed ADN decomposition
process. Filled and open symbols represent experimental
data obtained from two different batches of ADN samples.
Solid lines are kinetic modeling results with initial concentrations of NH3 4 1.21 mTorr, HN(NO2)2 4 1.21 mTorr
and N2O 4 0.11 mTorr. Dashed lines are kinetic modeling
results with initial concentrations of NH3 4 1.21 mTorr,
HN(NO2)2 4 1.10 mTorr, N2O 4 HNO3 4 0.11 mTorr.
Residence (reaction) time 4 19.1/T s (T in Kelvin) and
P 4 10 Torr with He as carrier gas.
between the modeled concentrations and the measured values is reasonably good, particularly for major products, NH3, N2O, and H2O. The underprediction of N2, which is a minor product, essentially
results from a slight overprediction of N2O.
Figure 5 presents the results of sensitivity analysis
for the three major species measured, NH3, H2O,
and N2O at 798 K. Only reactions that are sufficiently influential (3% that of the key process) are
included in the figure. The sensitivity coefficient is
defined as Sij(t) 4 ]Ci(t)/]kj 2 kj/Ci(t), where Ci(t)
is the concentration of species i at t and kj is the rate
constant of the jth reaction. As shown in Fig. 5, the
OH radical produced by reaction 3:
HNNO2 ` M 4 OH ` N2O ` M
(3)
and removed by reaction 5
OH ` NH3 4 H2O ` NH2
(5)
is the major reactive species.
In view of the fact that HNO3 has been shown to
be present in the gas phase [1] and in the condensed
phase in the form of AN, as already alluded to, in
our kinetic modeling we have tested the effect of
HNO3 on the rates of the decay of NH3 and of the
formation of N2, N2O, and H2O. By keeping the initial concentration of NH3 the same as measured at
373 K reactor temperature, the replacement of 9%
DN with HNO3, based on the initial concentrations
of N2O, led to no noticeable change in the predicted
HN(NO2)2 → HNNO2 ` NO2
HNNO2 ` M → OH ` N2O ` M
Chain propagation reactions:
OH ` NH3 → H2O ` NH2
NH2 ` NO2 → H2NO ` NO
NH2 ` NO → H ` N2 ` OH
Except for the decomposition of DN and HNNO2,
these reactions have been established through our
recent studies of the NHx (x 4 2,3) and NOy (y 4
1,2) systems [14,15,28,29]. The rate constant for the
DN decomposition (2) has been calculated as described by high-level ab initio MO and canonical variational RRKM theories. The predicted value as
given in Table 1 was used in the model without adjustment. The rate constant for the decomposition
of HNNO2, predicted to be in the second-order region as given in Table 1, was also calculated by cVRRKM theory based on the potential energy surface computed at the G2M//6-311G(d) level of
theory. The detail of the cVRRKM calculation for
this reaction will be presented elsewhere [27].
Under high-pressure conditions, the following
radical–radical reactions involving HNNO2 are expected to become significant because of the increasing concentrations of radical species:
HNNO2 ` OH → HNOH ` NO2
→ HNO ` HONO
HNNO2 ` NO → HNNO ` NO2
→ HONO ` N2O
HNNO2 ` NO2 → HNO ` N2O3 (or NO ` NO2)
→ HNO3 ` N2O
Kinetics and mechanisms of these bimolecular nitroamino radical reactions are not known. High-level
ab initio MO calculations are underway in our laboratory for preparation of the rate constant evaluation.
2356
PROPELLANTS
Fig. 5. Sensitivity analysis at 798
K. Conditions: NH3 4 1.21 mTorr,
HN(NO2)2 4 1.10 mTorr, N2O 4
HNO3 4 0.11 mTorr and P 4 10
Torr.
Summary
The absolute yields of N2, N2O, H2O, and NH3
measured in the thermal decomposition of ADN,
sublimed at 38 below melting point, could be satisfactorily accounted for with a mechanism consisting
of 152 reactions, assuming that initial concentrations
of NH3 are approximately equal to that of DN. The
substitution of 9% DN with HNO3, which was assumed to have the same concentration as the N2O
detected at reactor temperatures below 450 K (below which no reaction between the reactants was
observed), led to a slightly better agreement between experiment and the model.
The mechanism employed was established
through our earlier studies of the NHx (x 4 2,3) `
NOy (y 4 1,2) systems, with the addition of the
reactions involving DN and the nitro-amino
(HNNO2) radical whose rate constants were computed theoretically by means of ab initio MO/statistical-theory calculations.
Acknowledgments
J. Park and M. C. Lin gratefully acknowledge the support of this work from the Office of Naval Research (contract no. N00014-89-J-1949), and D. Chakraborty is thankful for the support to the Caltech Multidisciplinary
University Research Initiative under ONR grant no.
N00014-95-1-1388, program managers: Dr. Richard S.
Miller and J. Goldwasser. We are also grateful to Drs. A.
Stern and S. Caulder of Naval Surface Warfare Center for
providing the samples of ADN used in this study.
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